(* Project Euler Problem 47: Distinct primes factors
The first two consecutive numbers to have two distinct prime factors are:
14 = 2 × 7
15 = 3 × 5
The first three consecutive numbers to have three distinct prime factors
are:
644 = 2² × 7 × 23
645 = 3 × 5 × 43
646 = 2 × 17 × 19.
Find the first four consecutive integers to have four distinct prime
factors. What is the first of these numbers? *)
let isprime n = (n=2) || not (List.exists (fun d -> n%d=0) ([2]@[3..2..(int(sqrt(float n)))]))
let primes = [|for n in 2..2999 do if (isprime n) then yield n|]
let pfs x = Array.length (Array.filter (fun d -> x%d=0) (Array.takeWhile (fun p -> p < x/2) primes))
let pfsxyz x = ((pfs (x) = 4) && (pfs (x+1) = 4) && (pfs (x+2) = 4) && (pfs (x+3) = 4))
let consecutives upto = [for n in 1..upto do if (pfsxyz n) then yield n]
printfn "%O" (consecutives 150000)